stats psych 1-4

descriptive stats

simple statistics that describe situation

inferential stats

generalizing from a sample to a population

population

complete collection of observations or potential observations

sample

smaller collection of actual observations drawn from a population

random sampling

a sample should be randomly selected from a population in order to increase the likelihood that the sample accurately represents the population (drawing from a hat)

convenience sampling

students usually fall into WIERD category

random assignment

Random assignment signifies that each person has an equal chance of being assigned to any group in an experiment

types of data

qualitative, ranked, quantitative

Qualitative

a set of observations where any single observation is a word, letter, or numerical code that represents a class or category (categories/labels)

ranked

A set of observations where any single observation is a number that indicates relative standing

quantitative

A set of observations where any single observation is a number that represents an amount or a count (numerical values/intervals)

levels of measurement

nominal, ordinal, interval/ratio, nonphysical

nominal

Words, letters, or numerical codes of qualitative data that reflect differences in kind based on classification.

example: eye color

ordinal

Relative standing of ranked data that reflects differences in degree based on order
example: rank in contest

interval/ratio

these should have a true zero and equal intervals
example: depression levels

types of variables

discrete, continuous, approximate, idependent, dependent

discrete variable

A variable that consists of isolated numbers separated by gaps
example: # of siblings

continuous

A variable that consists of numbers whose values, at least in theory, have no restrictions
example: weight

approximate

rounding

independent variable

treatment manipulated by the investigator.

dependent variable

variable is believed to have been influenced by the independent variable

confounds

An uncontrolled variable that compromises the interpretation of a study.

frequency distribution

A collection of observations produced by sorting observations into classes and showing their frequency (denoted by the letter f) of occurrence in each class
- can be ungrouped or grouped

guidelines

req
- Each observation should be included in one, and only one, class.

• List all classes, even those with zero frequencies.

• All classes should have equal intervals.

• Book doesn’t mention – List in order from most to least

  • So “1” would be at the bottom and “10” would be at the top
    

optional
- All classes should have both an upper boundary and a lower boundary.

• Select the class interval from convenient numbers, such as 1, 2, 3, … 10, particularly 5 and 10 or multiples of 5 and 10.

• The lower boundary of each class interval should be a multiple of the class interval (130 is divisible by 10 which is the class interval).

• Aim for a total of approximately 10 classes.

constructing frequency distributions

• Range (245-133 is 112)

• Class interval (112/10 is 11.2)

• Round (11.2 to 10)

• Lowest Class begin and end (not 133 instead 130)

• Work upward (lowest number on bottom)

• Tally then replace with f

• Headings

relative frequency distributions

A frequency distribution showing the frequency of each class as a fraction of the total frequency for the entire distribution

cumulative frequency distributions

 a frequency distribution showing the total number of observations in each class and all lower-ranked classes

percentile ranks

Percentage of scores in the entire distribution with equal or smaller values than that score

positively skewed distribution

A distribution that includes a few extreme observations in the positive direction (to the right of the majority of observations)

• If mean is bigger than median, it's positively skewed

negatively skewed distribution

A distribution that includes a few extreme observations in the negative direction (to the left of the majority of observations)

• If median bigger than mean, it's negatively skewed

rounding

• Almost all stats in this class will be rounded to two decimal places

• .054 will round to .05

• .055 will round to .06

• .0545 will round to .05

p values

• p > .05 - accept the null

• p < .05 - reject the null

class interval

a defined range of numerical values within a dataset used to group data points into categories

leading zero

• If the statistic can be greater than 1, use a leading 0 (0.24 in)

• If the statistic cannot be greater than 1, do not use a leading 0 (p = .04)"

mode

the value of the most recent score (appears most often)

bimodal

Describes any distribution with two obvious peaks

• modes have to be exact same?

median

the middle value when observations are ordered from least to most

• formula: (n+1) / 2

mean

The mean is found by adding all scores and then dividing by the number of scores

population

A complete set of scores

• “mu” equals the sum of the variable X and is divided by the population size which is N

sample

A subset of scores

• X bar equals the sum of the variable X and is divided by the sample size which is n

sample size (n)

The total number of scores in the sample

not skewed

mean median mode will be similar

skewed (not symmetric)

mean is sensitive to outliers

FREQUENCY DISTRIBUTIONS FOR QUALITATIVE (NOMINAL) DATA

• Mean cannot be used with qualitative data.

• The median can be used whenever it is possible to order qualitative data from least to most because the level of measurement is ordinal

measures of variability

Descriptions of the amount by which scores are dispersed or scattered in a distribution

• Mean is a measure of position

• SD is a measure of distance

standard deviation

A rough measure of the average (or standard) amount by which scores deviate on either side of their mean

• Mean of deviations not useful

  • The sum of all scores, expressed as positive and negative deviations from the mean, always equals zero

degrees of freedom (df)

The number of values free to vary, given one or more mathematical restrictions

• The number of scores that are free to vary once the mean is fixed

methods for standard deviation

• First method is more intuitive, but can lead to rounding errors (left)

• Second method is less intuitive, but more precise (right)

standard deviation for samples

• Why n – 1?

  • Samples underestimate population variance